Optical rotation-sensitive devices were demonstrated by Sagnac and some other experimentalists with non-coherent light sources and with closed-path interferometers (triangular or multi-angular). These schemes belong to passive gyroscope types. Since the emergence of lasers, two new types of rotation-sensitive devices appeared: 1) passive type, with a laser replacing a lamp as an external light source; 2) active type, incorporating a laser inside a ring resonator, with the frequency difference between counterpropagating modes depending on the rotation rate Ω. In the first type of rotation-sensitive devices, the measured parameter is the phase shift between counterpropagating beams, whereas in the second type the measured parameter is the mode beating frequency Δv. The slope sensitivity of an active rotation-sensitive device is
      K    =                  ⅆ                  (                      Δ            ⁢                                                  ⁢            v                    )                            ⅆ        Ω              ,where K is also called the (gyroscopic) scaling factor, Ω is the angular rotation rate, and Δv can be represented as
                                          Δ            ⁢                                                  ⁢            v                    =                                    4              ⁢                                                          ⁢              A              ⁢                                                          ⁢              Ω                                                      n                g                            ⁢              λ              ⁢                                                          ⁢              L                                      ,                            (        1        )            where A is a ring area, L is its perimeter length, ng is the group index of the medium filling the resonator volume,
                                          n            g                    =                      n            +                                          v                ⁢                                  ⅆ                  n                                                            ⅆ                v                                                    ,                            (        2        )            and n is the refractive index of the same medium. It can be seen from Eq. (1) that the size parameter of A/L is very important to increase the slope sensitivity. This parameter depends on the shape of the ring. For a given area, A/L is maximum in a circular resonator, where for a circle of radius R we have
                              A          L                =                              R            2                    .                                    (        3        )            
Circular resonators can be easily realized with guiding structures, such as in optical fibers or optoelectronic integrated circuits (OEICs).
If R=1 cm (which is close to the physical limit for OEICs), K≈5000 in a ring filled with a typical semiconductor material, such as GaAs (ng≈4). An example of the conventional technique is the active rotation-sensitive hybrid ring laser, as shown in FIG. 1. The active element is a semiconductor optical amplifier 1, included inside an optical fiber loop 2. The frequency beating signal has been measured using a self-pickup technique, in the form of voltage oscillations appearing in the pumping circuitry of the semiconductor optical amplifier. This technique is based on the phenomenon of electrical response to the light intensity inside the active region of a laser or amplifier. The frequency beating between counterpropagating modes leads to oscillations of local light intensity and corresponding oscillations in electrical voltage. Detecting these oscillations gives the beating frequency and the rotation rate. In the scheme of FIG. 1, the semiconductor optical amplifier occupies only a small part of the ring length (about 1 mm in a 15-cm long loop). In contrast, in a monolithically integrated semiconductor ring, its whole length is filled with a semiconductor medium containing a p-n junction. In this case, the pickup technique should be modified, and the beating signal will not be obtained with a single electrode to the whole ring. To increase the slope sensitivity K, the size of the ring cavity can be increased in terms of the factor A/L. However, due to technological limitations, only a small improvement in gyro sensitivity can be expected using this approach. The present invention embodies the potential for a dramatic increase in slope sensitivity using the nonlinear Sagnac effect (NLSE), by exploiting nonlinear mode interactions in semiconductor lasers that can produce effective group indices close to zero.
The NLSE is a phenomenon deviating from normal Sagnac effect due to a change in the refractive index dispersion
            ⅆ      n              ⅆ      v        ,caused by parametric interactions of waves in a nonlinear medium (such as in semiconductor lasers). In a strong electromagnetic field, the optical parameters are perturbed in the vicinity of a strong wave frequency. A relatively small perturbation of the refractive index n (10−3-10−4) that occurs over a very narrow spectral range (frequency range of 1010-1011 s−1), produces a substantial perturbation of the refractive index dispersion
                    ⅆ        n                    ⅆ        v              ⁢          (                        10          10                -                              10            11                    ⁢                      s                          -              1                                          )        ,comparable to its linear part. This means that in the range where the induced nonlinear dispersion is negative, it can compensate or even overcompensate the linear (positive) part and give the total dispersion close to zero or even negative. The result is a significant increase in the beating frequency (1), due to ng approaching zero. The spectral point where ng→0 is sometimes called the point of critically anomalous dispersion (CAD). In the vicinity of this point, superluminal light propagation, with the group velocity significantly higher than the speed of light in vacuum c, must be taken into account. Features of the CAD point are that the group index ng passes through zero, and the group velocity has a discontinuity, going to infinite values of opposite signs depending on which side the CAD point is approached from. The usual identification of the photon velocity with the group velocity of light is not working in this case, and a commonly accepted approach of wave packets is not valid. In order to use the NLSE in practice for an increase in the rotation sensitivity, the operation point should be chosen not at the CAD point but in its close vicinity (in the superluminal range). It corresponds to a usage of the so called fast light.
The frequency shift associated with the perturbation of the refractive index in the vicinity of the frequency vs of the driving wave can be shown to be given by the following expression:
                                          Δ            ⁢                                                  ⁢            v                    =                                    (                                                4                  ⁢                                                                          ⁢                  A                  ⁢                                                                          ⁢                  Ω                                L                            )                        ×                                          {                                                      λ                    ⁢                                                                                  ⁢                                          n                                              g                        ,                        lin                                                                              -                                                            (                                              2                        ⁢                                                                                                  ⁢                        π                        ⁢                                                                                                  ⁢                        cC                        ⁢                                                                                                                                        E                              0                                                                                                            2                                                                    )                                        ⁢                                                                  (                                                  1                          -                                                      2                            ⁢                                                                                                                  ⁢                            α                            ⁢                                                                                                                  ⁢                            x                                                    -                                                      x                            2                                                                          )                                            /                                              [                                                                              γ                            2                                                    ⁡                                                      (                                                          1                              +                                                              x                                2                                                                                      )                                                                          ]                                                              ⁢                    2                                                  }                                            -                1                                                    ,                            (        4        )            where C=−B(N−N0)(de″/dN)/(2n), N0 is the carrier density, N0 is the transparency carrier density, ∈″ is the imaginary part of the dielectric constant, γ is the carrier relaxation rate, B is the bimolecular recombination coefficient (in units of m2/V2s), α is the line width broadening factor, x=2π(vs−v)/γ is the normalized detuning with respect to the strong wave frequency vs, and ng,linis the linear (unperturbed) component of the group index.